Question: Solve for $x$ and $y$ using elimination. ${-2x-6y = -38}$ ${2x+5y = 33}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-y = -5$ $\dfrac{-y}{{-1}} = \dfrac{-5}{{-1}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-2x-6y = -38}\thinspace$ to find $x$ ${-2x - 6}{(5)}{= -38}$ $-2x-30 = -38$ $-2x-30{+30} = -38{+30}$ $-2x = -8$ $\dfrac{-2x}{{-2}} = \dfrac{-8}{{-2}}$ ${x = 4}$ You can also plug ${y = 5}$ into $\thinspace {2x+5y = 33}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(5)}{= 33}$ ${x = 4}$